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A boat is sailing about 400 feet from the cliff at the shore of a lake. A sailor on the boat uses a device to measure the angle of elevation between the lake level and the top of the cliff. He draws a diagram like the one below. Using his measurements, find the height of the cliff to the nearest thousandth.

A boat is sailing about 400 feet from the cliff at the shore of a lake A sailor on the boat uses a device to measure the angle of elevation between the lake lev class=

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altavistard
Note that tan 15 deg = h / (400 ft)

tan 15 deg = 0.2679, so  (400 ft)(0.2679) = 107 ft

The height of the cliff is approx 107 ft.  I don't think it reasonable to try to specify the height to the nearest thousandth of a foot.

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